alt Hacker Newsspecifically avoid resources written by and for physicists.
the model of quantum mechanics, if you can afford to ignore any real-world physical system and just deal with abstract |0>, |1> qubits, is relatively easy. (this is really funny given how incredibly difficult actual quantum physics can be.)
you have to learn basic linear algebra with complex numbers (can safely ignore anything really gnarly).
then you learn how to express Boolean circuits in terms of different matrix multiplications, to capture classical computation in this model. This should be pretty easy if you have a software engineer's grasp of Boolean logic.
Then you can learn basic ideas about entanglement, and a few of the weird quantum tricks that make algorithms like Shor and Grover search work. Shor's algorithm may be a little mathematically tough.
realistically you probably will never need to know how to program a quantum computer even if they become practical and successful. applications are powerful but very limited.
"What You Shouldn't Know About Quantum Computers" is a good non-mathematical read.